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Calculations are carried out by the FEM with the use of the non-linear-plastic material model with stiffness degradation.
This model is a deformation-based continuum damage model with stiffness degradation and is based on a deformation equivalent principle and generalized force deformation relationships for concrete and its steel reinforcement.
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A combination of Maxwell and Voigt models, with stiffness and damping variable according to the stress and strain rate, to represent nonlinear material responses, is coupled to a relaxation model, in order to represent the Mullins effect (the rubber mechanical behavior also depends on load history).
The closed-loop system is modelled with elastic stiffness, active stiffness introduced by isotropic actuator lamina and geometric stiffness due to stresses developed by hygrothermal strain.
A shakedown-frame plastic moments minimization and load-optimization nonlinear mathematical model with strength, stiffness, and stability constraints is investigated.
The nonlinear model with cubic stiffness used in this work produces a transmissibility curve which is fitted using the least squares method to the experimentally obtained transmissibility curve.
A lumped mass parameter model with variable stiffness is established to investigate the vibration performance of the gripper cylinder in TBM.
In the 6-story building model LS4 with stiff lateral stiffness, the story shear, displacement, and inter-story drift calculated from the ESL method closely match the average response calculated from the time history method.
Then two static displacement models with different stiffness definitions are established and mathematically proved to be equivalent, both of which may be versatile for practical applications.
On the other hand, the explicit schema might require much smaller time steps compared to implicit integration alternative especially for models with high stiffness and low mass density.
The damages of intra-ply fiber and matrix are initiated with stress failure criteria and progressive damage propagation is modeled with a stiffness discount method and energy criteria.
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